Expectancy Tables
Reign H. Bittner, Carlton Eugene Wilder · The Journal of Experimental Education · 1946
The product moment correlation coefficient is commonly used by research workers as a statistical measure of the relationship between two measures of a group of individuals. In applied psychology this statistic is often used to define the correspondence between scores on tests or other measures of traits and apti tudes and a criterion of proficiency on a job, in a training course in school or industry, or some other activity. In this case the ultimate objective is to evaluate the criterion poten tialities of an individual or a group on the basis of other data. It is often desirable and sometimes neces sary to present the results of correlation anal ysis to the layman. However, the concept of correlation is difficult to interpret to the non technically trained person. In addition, the coefficient itself provides neither the techni cian nor the layman with a concrete evalua tive statement of the expected criterion per formance of individuals with given scores on the associated variable. Accordingly, a method is needed for reinterpreting correlation coeffi cients in terms of the predictive significance of the association expressed in terms of simple mathematical concepts which are uni versally understood.1 Taylor and Russell (4) have developed tables for interpreting certain correlation coefficients in terms of the proportion of the selected group who will be expected to be suc cessful if a given percent of the total group is considered successful on the basis of a mini mum criterion score and a given percent of the total group is selected on the basis of a minimum score on the predictor variable. This method has considerable merit for interpret ing the correlation coefficient in terms of its predictive significance if one is interested only 1 Various functions of the correlation coefficient such as the coefficient of alienation, k, the coefficient of forecasting effi ciency, E, and the coefficient of determination, r2, have been used to aid in the interpretation of the correlation coefficient but none of these are superior to the coefficient itself for these purposes. in group predictions and if it can be assumed that the correlation surface is normal. How